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For the local-type primordial perturbation, it is known that there is aninequality between the bispectrum and the trispectrum. By using thediagrammatic method, we develop a general formalism to systematically constructthe similar inequalities up to any order correlation function. As anapplication, we explicitly derive all the inequalities up to six andeight-point functions.

Extension of local-type inequality for the higher order correlation functions